Yes, you can. In order to make that you should log in to your Apple Game Center account first. Then open the game, go to Your Office (icon with the suitcase) and choose Sync and Continue button. So your progress will be saved on your Game Center account and you will be able to continue your game from any other device. Even if your game is on iPad you can easily sync it with your iPhone. Game Center account can also be switched right through the game. Open Your Office and tap Change Game Center account.
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